Recursive Method for Nekrasov partition function for classical Lie groups

TL;DR

This paper introduces a recursive approach to compute Nekrasov partition functions for classical Lie groups, providing a new method to derive closed-form expressions from integral definitions.

Contribution

It presents a recursion formula for Nekrasov partition functions applicable to classical Lie groups, facilitating the derivation of closed expressions from integral representations.

Findings

Derived a recursion relation from the integral definition of partition functions.

Obtained a closed-form expression for a factor related to generalized Young diagrams.

Applied the method to a toy model reflecting BCD type Lie groups.

Abstract

Nekrasov partition function for the supersymmetric gauge theories with general Lie groups is not so far known in a closed form while there is a definition in terms of the integral. In this paper, as an intermediate step to derive it, we give a recursion formula among partition functions, which can be derived from the integral. We apply the method to a toy model which reflects the basic structure of partition functions for BCD type Lie groups and obtained a closed expression for the factor associated with the generalized Young diagram.